Reasoning with Uncertainty in Deductive Databases and Logic Programs

Abstract

Of all scientific investigations into reasoning with uncertainty and chance, probability theory is perhaps the best understood paradigm. Nevertheless, all studies conducted thus far on the semantics of quantitative logic programming have been restricted to non-probabilistic semantical characterizations. In this paper, we survey the major features and summarize the major results of the various frameworks that we have developed to rectify this situation. In the first part of this paper, we outline a deductive database framework which is expressive enough to represent such probabilistic relationships as conditional probabilities, Bayesian updates, probability propagation and mutual exclusion. We propose a fixpoint theory and a probabilistic model theory, and characterize their inter-relationships. As the aforementioned language is monotonic in nature, we discuss in the second half of this paper three approaches of supporting non-monotonic probabilistic reasoning. In the first approach, we use a non-monotonic negation operator. In the second, we use the Dempster-Shafer rule of combination. Finally, we discuss how empirical probabilities can be supported in monadic deductive databases.